Fermionic back-reaction on kink and topological charge pumping in the $sl(2)$ affine Toda coupled to matter

TL;DR

This paper investigates how fermionic back-reaction influences topological charge pumping and kink properties in an $sl(2)$ affine Toda model coupled to matter, revealing new bound states, scattering effects, and charge dynamics.

Contribution

It introduces a detailed analysis of fermion back-reaction on kinks in the $sl(2)$ affine Toda model, including new parametrizations and the discovery of a charge pumping mechanism.

Findings

Fermionic back-reaction alters kink properties significantly.

Identification of fermion bound states and scattering states localized on kinks.

Discovery of a topological charge pumping mechanism induced by fermionic effects.

Abstract

We explore the Faddeev-Jackiw (F-J) symplectic Hamiltonian reduction of the $sl(2)$ affine Toda model coupled to matter (ATM), which includes new parametrizations for a scalar field and a Grassmannian fermionic field. The structure of constraints and symplectic potentials primarily dictates the strong-weak dual coupling sectors of the theory, ensuring the equivalence between the Noether and topological currents. The analytical calculations encompass the fermion-kink classical solution, the excited fermion bound states localized on the kink, and the scattering states, all of which account for the fermion back-reaction on the soliton. The total energy, which includes the classical fermion-soliton interaction energy, the bound-state fermion energy, and the fermion vacuum polarization energy (VPE), is determined by the topological charge of the kink. This system satisfies first-order differential equations and a chiral current conservation equation. Our results demonstrate that the excited fermion bound states and scattering states significantly alter the properties of the kink. Notably, they give rise to a pumping mechanism for the topological charge of the in-gap kink due to fermionic back-reaction, as well as the appearance of kink states in the continuum (KIC).